A pilot sample of 75 items was​ taken, and the number of items with the attribute of interest was found to be 30. How many more items must be sampled to construct a 99​% confidence interval estimate for p with a 0.025 margin of​ error?

Answer: 2474Step-by-step explanation:Given : A pilot sample of 75 items was​ taken, and the number of items with the attribute of interest was found to be 30.Then, prior estimate for proportion of attribute of interest: [tex]p=\dfrac{30}{75}=0.4[/tex]Significance level : [tex]\alpha: 1-0.99=0.01[/tex]Critical value : [tex]z_{\alpha/2}=2.576[/tex]Margin of error : [tex]E=0.025[/tex]The formula use to find the sample size :_ [tex]n=p(1-p)(\dfrac{z_{\alph/2}}{E})^2\\\\\Rightarrow\ n=(0.4)(1-0.4)(\dfrac{2.576}{0.025})[/tex]Now, simplify , we get[tex]n=2548.137984\approx2549[/tex]Now, the number of items more to sample = [tex]2549-75=2474[/tex]